Grade 5
Unit 3 Multiplication and Division of Fractions
Mathematics
Unit Goals – Stage 1
Number of Days: 34
Traditional: November 30, 2016 – January 31, 2017 Track B: November 30, 2016 – February 10, 2017
Unit Description: In Unit 3 students extend their understanding of multiplying a fraction by a whole number to multiplying fractions by fractions. Students
use line plots and other tools to reason about problem situations. In preparation for grade six work in ratios and proportional reasoning, students interpret
multiplication as scaling (resizing). Students use their understanding of the relationship of multiplication and division to develop a conceptual
understanding of division with fractions (division of a whole number by a unit fraction and a unit fraction by a whole number).
Materials: concrete and visual fraction models (i.e. fraction strips, fraction circles, pattern blocks, color tiles), index cards, 1 in. and 1 cm grid paper,
colored pencils, GoMath! MathBoard or whiteboard
Standards for Mathematical Practice
Transfer Goals
Students will be able to independently use their learning to…
SMP.1
Make sense of problems and
• Make sense of never-before-seen problems and persevere in solving them.
persevere in solving them.
• Construct viable arguments and critique the reasoning of others.
SMP.2
Reason abstractly and quantitatively.
SMP.3
Construct viable arguments and
Making Meaning
critique the reasoning of others.
UNDERSTANDINGS
ESSENTIAL QUESTIONS
SMP.4
Model with mathematics.
Students will understand that…
Students will keep considering…
SMP.5
Use appropriate tools strategically.
• Division is equal sharing.
• How does a fraction represent division?
SMP.6
Attend to precision.
• The area model, fraction strips, number lines, • How do I use models to show understanding
SMP.7
Look for and make use of structure.
and counters can be used to show fraction
of fractions?
SMP.8
Look for and express regularity in
multiplication.
• How is what we understand about
repeated reasoning.
• Multiplying a number by a fraction is scaling,
multiplication of whole numbers useful when
or resizing that number.
multiplying fractions?
Standards for Mathematical Content
Clusters Addressed
Acquisition
KNOWLEDGE
SKILLS
Number and Operations - Fractions
Students will know…
Students will be skilled at and/or be able to…
5.NF.B
Apply and extend previous
• The definitions of the academic vocabulary
• Interpret a fraction as division of the
understandings of multiplication and
words such as conversion, line plot, part of a
numerator by the denominator (a/b = a ÷ b).
division to multiply and divide
group, resizing, and scaling.
•
Use
visual models or equations to solve
fractions.
• The general formula to multiply fractions.
fraction multiplication problems.
• Create real world problems involving
Measurement and Data
multiplication of fractions.
5.MD.B
Represent and interpret data.
• Divide unit fractions by whole numbers and
whole numbers by unit fractions.
• Solve word problems involving fractions.
• Find the area of a rectangle with fractional
and whole number side lengths.
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
1
Posted 6/10/16
Grade 5
Unit 3 Multiplication and Division of Fractions
Mathematics
Assessed Grade Level Standards
Standards for Mathematical Practice
SMP.1
SMP.2
SMP.3
SMP.4
SMP.5
SMP.6
SMP.7
SMP.8
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Standards for Mathematical Content
Number and Operations – Fractions
[m]
5.NF.B
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.3
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole
numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the
problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are
shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight,
how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
5.NF.4
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a
× q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same
with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and
show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of
rectangles, and represent fraction products as rectangular areas.
5.NF.5
Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated
multiplication.
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number
(recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a
fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n ×
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
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Posted 6/10/16
Grade 5
Unit 3 Multiplication and Division of Fractions
Mathematics
Assessed Grade Level Standards
a)/(n × b) to the effect of multiplying a/b by 1.
5.NF.6
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to
represent the problem.
5.NF.7
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for
(1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that
(1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5),
and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that
4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit
fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each
person get if 3 people share ½ lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
[s]
5.MD.B
Represent and interpret data.
5.MD.2
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to
solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find
the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Key: [m]= major clusters; [s] = supporting clusters; [a] = additional clusters
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
3
Posted 6/10/16
Grade 5
Unit 3 Multiplication and Division of Fractions
Mathematics
Evidence of Learning – Stage 2
Assessment Evidence
Unit Assessment
Students will complete selected response and constructed response items to indicate level of mastery/understanding of the unit standards as outlined in
this guide.
[m] 5.NF.B
• The student interprets a fraction as division of the numerator by the denominator.
• The student solves problems involving division of whole numbers leading to quotients in the form of fractions or mixed numbers, with or without
fraction models.
• The student multiplies a fraction or whole number by a fraction.
• The student multiplies fractional side lengths to find areas of rectangles.
• The student compares the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated
multiplication.
• The student solves real-world problems involving multiplication of fractions and mixed numbers, with or without visual fraction models.
• The student solves real-problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions,
with or without visual fraction models.
[s] 5.MD.B
• The student completes or identifies a line plot with fractional units to display a data set.
• The student uses operations on fractions to solve problems involving information presented in line plots.
For selected content, students will need to…
• Solve complex problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.
• Clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others.
Other Evidence
Formative Assessment Opportunities
• Opening Tasks
• Go Math! Show What You Know
• Classroom Challenges
• Go Math! Performance Task
• Homework (Go Math! Standards Practice Book)
• Go Math! Getting Ready for the Smarter Balance
• Go Math! Chapter Test (Assessment Guide)
• Go Math! Chapter Review / Test – Student Book
•
•
•
•
•
•
•
•
Exit slips
Extension Menus
It’s All About the Facts Supplemental materials
In-class projects
Recorded Teacher Observations
Writing activities
Quizzes
SBAC Interim Assessment Block (IAB)
Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website – “M” Mathematics – Curriculum Documents
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
4
Posted 6/10/16
Grade 5
Unit 3 Multiplication and Division of Fractions
Mathematics
Learning Plan – Stage 3
Days
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Learning Target
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math
(Universal Access for SPED, Struggling
Students, ELL, GATE)
•
•
•
Saying facts orally.
Writing fact families.
Using them to play games.
•
I can use mental
math strategies
to add, subtract,
multiply and
divide by…
•
•
Participating in daily Number Talks.
Communicating my reasoning.
•
90
minutes
per week
(Schools/
grades
with ST
Math)
I will persevere
in problem
solving as I play
interactive
games to help
me understand
math by…
•
Before
the Unit
(as
needed)
I can show what
I know about
multiplying and
dividing fractions
by…
Daily
Daily
I will know basic
math facts by…
Maintaining Fluency Through
Fact Families, pp. 1 –10, 13 –
28, 31
Go Math! Strategies and
Practice for Skills and Facts
Fluency
•
Basic Facts Game: “Math
Cards”
https://www.youcubed.org/tas
k/math-cards/
Number Talks Strategies and
Problem Sets, Grades 2-5
(also found on intranet in
Instructional Tools)
•
Fraction Number Talks
(Instructional Tools –
Elementary – Number Talks)
Calendar Math (from Unit 1)
Multiple Markers for 100 Days
(from Unit 1)
ST Math Objectives
• The Number Line
• Fraction Multiplication
• Fraction Division
•
Developing long term problem solving
skills.
Visualizing math concepts.
Making connections between concepts
and across grades.
Playing interactive games.
•
Completing “Show What You Know”.
•
•
•
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
•
Intranet - Instructional Tools –
Elementary – 5th Grade)
•
•
ST Math Tips
• Set goals: 3% progress per
week
• Review your classroom reports
regularly
• Monitor/Celebrate progress
• Monitor/Intervene students with
alerts
• Assign a few homework
objectives at a time
Ch. 7 & 8 “Show What You
Know”, pp. 305 & 355
**Use the Diagnostic Table if
needed for intervention options:
On-level, Strategic, Intensive, and
Independent.
5
Posted 6/10/16
Grade 5
Unit 3 Multiplication and Division of Fractions
Mathematics
Learning Plan – Stage 3
Days
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Learning Target
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math
(Universal Access for SPED, Struggling
Students, ELL, GATE)
1
I can solve word
problems
involving
fractions by…
•
•
•
OPENING TASK – Sharing Pizza
• Using manipulatives to solve a real
world problem.
• Using equal sharing.
•
2–3
I can interpret a
fraction as
division of the
numerator by the
denominator
by…
•
•
•
•
Solving word problems and creating
story contexts to represent problems
involving division of whole numbers.
Using equal sharing to write the
amounts in a division problem as a
fraction.
Partitioning amounts, connecting to the
meaning of multiplication by a unit
fraction (i.e. 5 objects shared equally
among 3 means each of the 5 objects
Intranet - Instructional Tools –
Elementary – 5th Grade)
Sharing Pizza Task
Sharing Pizza Teacher Guide
Ch. 7 & 8 “Math Detective”, pp.
305 & 355
Ch. 7 & 8 “Vocabulary Builder”,
pp. 306 & 356
o Note: These activities
should be used as a
formative assessment for
this unit.
•
Lesson 8.3: Connect Fractions
to Division
•
•
•
•
•
•
See www.illustrativemathematics.org/5
for fraction tasks and videos to
be used throughout the unit.
Engage, Explore, Evaluate
Problems (to use throughout the
unit)
Notice and Wonder Introduction
and Record Sheet (to use
throughout the unit, Instructional
Tools – Notice and Wonder)
Cooking Time Lesson
How Much Pie? Task
Sharing Lunches Task
What is 23 ÷ 5? Task
contributes 1 of itself to each share so
3
so 5 ÷ 3 = 5 × 1 = 5 )
•
•
3
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
3
Using concrete manipulatives, fraction
models, tape diagrams, drawings,
equations and explanations.
Interpreting the quotient in the context
of the problem (writing quotients as
fractions or mixed numbers).
6
Posted 6/10/16
Grade 5
Unit 3 Multiplication and Division of Fractions
Mathematics
Learning Plan – Stage 3
Days
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Learning Target
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math
(Universal Access for SPED, Struggling
Students, ELL, GATE)
4-9
I can solve word
problems and
create story
contexts for
problems
involving
multiplication of
whole numbers
and fractions
by…
•
•
•
Start with
Extending understanding of
multiplication with whole numbers to
multiplication with fractions.
Using fraction strips, number lines and
area models.
Converting a whole number to a
•
•
fraction (i.e. 4 = 4 ).
1
•
Intranet - Instructional Tools –
Elementary – 5th Grade)
•
Lesson 7.1: Find Part of Group
Lesson 7.2: Multiply Fractions
and Whole Numbers
Lesson 7.3: Fraction and
Whole Number Multiplication
•
•
•
•
10 - 12
I can solve word
problems and
create story
contexts for
problems
involving
multiplication of
fractions by…
•
•
•
•
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
•
•
Extending understanding of
multiplication with whole numbers to
multiplication with fractions.
Using fraction strips, number lines and
area models.
Multiplying the numerator by the
numerator and the denominator by the
denominator.
Simplifying according to the context of
the problem (see note in Supplemental
Resources).
Lesson 7.4 Multiply Fractions
Lesson 7.6 Fraction
Multiplication
•
•
•
Problem Solving-Grades 3-5:
Tasks 4.6 – 4.8, pp. 72-73
o Problem Solving Tasks 4.6,
4.7 & 4.8 (Use these tasks
together so students
understand that context
drives whether we are
working with an equal group
of fractional parts or the
fractional part of a set. The
same numbers are used in
all of these tasks.)
Raspberry Cake Task
Enlarge a Recipe – Banana
Bread Task
o myPD Video Course#2760
“Formative Assessment with
Problem Solving”
Good Questions, p. 28 #6
Math Solutions Lesson by
Marilyn Burns “Introducing
Multiplication of Fractions”
http://mathsolutions.com/doc
uments/0-941355-64-0_L.pdf
Cornbread Fundraiser Task
Folding Strips of Paper Task
Multiply Fractions Card Game
Simplifying does not need to be
taught in isolation; rather it should
be addressed according to the
context of the problem. Grade 5
students should be able to simplify
fractions based on their prior work
with equivalent fractions. CA
7
Posted 6/10/16
Grade 5
Unit 3 Multiplication and Division of Fractions
Mathematics
Learning Plan – Stage 3
Days
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Learning Target
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math
(Universal Access for SPED, Struggling
Students, ELL, GATE)
Intranet - Instructional Tools –
Elementary – 5th Grade)
Mathematics Framework on p.21
http://www.cde.ca.gov/ci/ma/cf/documen
ts/grade4mathfw.pdf
13 - 16
I can tell the size
of a product
based on the
factors (relative
to 1) by…
•
•
•
17 - 19
20 - 21
22 - 27
I can find the
area of a
rectangle with
fractional side
lengths by…
•
I can solve realworld problems
involving
multiplication of
fractions and
mixed numbers
by…
I can solve realworld problems
involving division
of unit fractions
by whole
numbers and
whole numbers
by unit fractions
by…
•
•
•
•
•
•
•
•
•
•
•
•
Extending understanding of division
with whole numbers to fractions.
Using visual fraction models to show
the quotient.
Using the relationship between
multiplication and division.
Using equations to show the problem.
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
•
Seeing that multiplication by numbers
bigger than 1 produces a larger
quantity without performing the
multiplication.
Seeing that multiplication by a number
smaller than 1 produces a smaller
quantity without performing the
multiplication.
Seeing that multiplication by 1 leaves
the quantity unchanged.
Tiling the rectangle with unit squares of
the appropriate unit fraction side
lengths.
Multiplying the side lengths.
Representing fraction products as
rectangular areas.
Explaining and illustrating the solution.
Using visual fraction models or
equations.
•
•
•
8
Lesson 7.5 Compare Fraction
Factors and Products
Lesson 7.8 Compare Mixed
Number Factors and Products
•
Fundraising Task
Area and Mixed Numbers
Lesson
Lesson 7.7: Investigate - Area
and Mixed Numbers
•
•
Chavone’s Bathroom Tiles Task
Good Questions, p. 29 #7
Lesson 7.9: Multiply Mixed
Numbers
•
•
•
Making Cookies Task
Bake Sale Performance Task
Improving Our School
Performance Task
Start with
•
Divide Fractions Model 5E
Lesson
Problem Solving-Grades 3-5
Tasks 4.9 & 4.10 pp. 74-75
o Problem Solving Tasks 4.9 &
4.10 (Use these tasks
together so students
understand both partitive and
measurement fraction
•
Lesson 8.1: Investigate Divide Fractions and Whole
Numbers
Lesson 8.4: Fraction and
Whole-Number Division
Lesson 8.5: Interpret Division
Posted 6/10/16
Grade 5
Unit 3 Multiplication and Division of Fractions
Mathematics
Learning Plan – Stage 3
Days
Learning Target
Suggested Sequence of Key Learning Events and Instruction
Core Resources:
Success Criteria
Go Math!
http://www-k6.thinkcentral.com
Supplemental Resources:
Books, Internet and
Curriculum Intranet (LBUSD Math
(Universal Access for SPED, Struggling
Students, ELL, GATE)
•
28 - 29
I can use my
understanding of
multiplication
and division to
multiply and
divide fractions
in a real world
situation by…
30 - 32
I can solve
problems using
data from line
plots with
fraction
measurements
by…
33
34
•
FORMATIVE ASSESSMENT LESSON
Classroom Challenge: Baker Brenda’s
Bread
• Applying and extending my previous
understanding of multiplication and
division.
• Communicating my reasoning.
• Checking to see if my answers make
sense.
• Creating line plots.
• Identifying fractional units of a data set.
• Using operations on fractions from the
information presented in a line plot.
with Fractions
Lesson 8.2: Problem Solving:
Use Multiplication
FAL, Baker Brenda’s Bread
(Intranet - Assessment)
Intranet - Instructional Tools –
Elementary – 5th Grade)
•
•
•
•
division.)
Dog Food Task
Good Questions, p. 29 #8
Musical Notes Writing Activity
Soccer Snacks Performance
Task
•
Baker Brenda’s Bread - FAL,
Differentiated Activities
•
•
Fractions on a Line Plot Task
Line Plots Lesson
Unit Assessment
Chapter 8 Performance Task – “Trail Teamwork” (Assessment Guide, pp. AG145 – 149D)
At this point, all standards addressed in the Grade 5 Interim Assessment Block – “Fractions” have been covered.
This block may now be administered.
We would appreciate feedback on the following:
Unit Guide bit.ly/Grade5UnitGuide
Assessment and FAL bit.ly/Grade5Assessment
LONG BEACH UNIFIED SCHOOL DISTRICT
New 2016 – 2017
9
Posted 6/10/16